Bunuel wrote:
A circle with center (1, 0) and radius 2 lies in the coordinate plane shown above. If point (x, y) lies on the circle, is (x, y) in quadrant II?
(1) |y| < 1
(2) |x| < 1
Target question: Is (x, y) in quadrant II? Given: A circle with center (1, 0) and radius 2 lies in the coordinate plane Let's
sketch the circle along with some key points on the circle:
From here, let's jump to . . . .
Statements 1 and 2 combined There are several points on the circles that satisfy BOTH statements. Here are two cases:
Case a: The point lies slightly above and to the right of (-1,0).
Notice that the x-coordinate is between -1 and 0, so we can be certain that |x| < 1
Likewise, the y-coordinate is slightly greater than 0, which means |y| < 1
In this case, the answer to the target question is
YES, the point (x,y) IS in quadrant IICase b: The point lies slightly below and to the right of (-1,0).
Notice that the x-coordinate is between -1 and 0, so we can be certain that |x| < 1
Likewise, the y-coordinate is slightly less than 0, which means |y| < 1
In this case, the answer to the target question is
NO, the point (x,y) is NOT in quadrant IISince we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
_________________
Test confidently with gmatprepnow.com